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1. US20200057611 - Method for generating a prime number by testing co-primalty between a prime candidate and a predetermined prime number in a binary base

Office
United States of America
Application Number 16486904
Application Date 09.02.2018
Publication Number 20200057611
Publication Date 20.02.2020
Grant Number 11281433
Grant Date 22.03.2022
Publication Kind B2
IPC
G06F 7/72
GPHYSICS
06COMPUTING; CALCULATING OR COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations
72using residue arithmetic
H04L 9/00
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
H04L 9/30
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
28using particular encryption algorithm
30Public key, i.e. encryption algorithm being computationally infeasible to invert and users' encryption keys not requiring secrecy
CPC
H04L 9/002
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Cryptographic mechanisms or cryptographic; arrangements for secret or secure communication
002Countermeasures against attacks on cryptographic mechanisms
G06F 7/72
GPHYSICS
06COMPUTING; CALCULATING; COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations ; , e.g. using difunction pulse trains, STEELE computers, phase computers
72using residue arithmetic
H04L 9/3033
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Cryptographic mechanisms or cryptographic; arrangements for secret or secure communication
30Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
3006underlying computational problems or public-key parameters
3033details relating to pseudo-prime or prime number generation, e.g. primality test
G06F 2207/7204
GPHYSICS
06COMPUTING; CALCULATING; COUNTING
FELECTRIC DIGITAL DATA PROCESSING
2207Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
72Indexing scheme relating to groups G06F7/72 - G06F7/729
7204Prime number generation or prime number testing
Applicants THALES DIS FRANCE SA
Inventors Alexandre Berzati
Myléne Roussellet
Agents The Jansson Firm
Pehr B. Jansson
Priority Data 17305191 21.02.2017 EP
Title
(EN) Method for generating a prime number by testing co-primalty between a prime candidate and a predetermined prime number in a binary base
Abstract
(EN)

The present invention relates to a method for generating a prime number and using it in a cryptographic application, comprising the steps of: a) determining at least one binary base B with a small size b=log2(B) bits and for each determined base B at least one small prime pi such that B mod pi=1, with i an integer, b) selecting a prime candidate YP, c) decomposing the selected prime candidate YP in a base B selected among said determined binary bases : YP=ΣyjBid) computing a residue yPB from the candidate YP for said selected base such that yPByje) testing if said computed residue yPB is divisible by one small prime pi selected among said determined small primes for said selected base B, f) while said computed residue yPB is not divisible by said selected small prime, iteratively repeating above step e) until tests performed at step e) prove that said computed residue yPB is not divisible by any of said determined small primes for said selected base B, g) when said computed residue yPB is not divisible by any of said determined small primes for said selected base B, iteratively repeating steps c) to f) for each base B among said determined binary bases, h) when, for all determined bases B, said residue yPB computed for a determined base is not divisible by any of said determined small primes for said determined base B, executing a known rigorous probable primality test on said candidate YP, and when the known rigorous probable primality test is a success, storing said prime candidate YP and using said stored prime candidate YP in said cryptographic application.